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Geometry: Chapter 3

Geometry: Chapter 3. Ch. 3.3: Use Parallel Lines and Transversals. Postulate 15: Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 154.

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Geometry: Chapter 3

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  1. Geometry: Chapter 3 Ch. 3.3: Use Parallel Lines and Transversals

  2. Postulate 15: Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 154.

  3. Ex. 1 Identify Congruent Angles The measure of three of the numbered angles is 550. Identify the angles. Explain your reasoning. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.

  4. Theorem 3.4 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.

  5. Theorem 3.5 Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.

  6. Theorem 3.6 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.

  7. Theorem 3.7: Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. If h || k, and j┴ h, then j┴ k. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.

  8. Ex. 2 Use properties of parallel lines. Find the value of x. Solution: By the Corresponding Angles Postulate, the angle with a m135o and the angle with a m(x -30)o are congruent. Using the definition of congruent angles, the two angle measures are equal. 135o= (x -30)o 135+30=x 165=x Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.

  9. Ex. 3. Prove that if two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 156.

  10. Ex. 4 Determine which other lines, if any, must be perpendicular. Explain your reasoning. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.

  11. Ex. 4 Determine which other lines, if any, must be perpendicular. Explain your reasoning. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.

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